文献类型：期刊文献

英文题名：Measurable Sensitivity for Semi-Flows

作者：Quan, Weizhen[1];Lu, Tianxiu[2];Li, Risong[3];Chen, Yuanlin[2];Ding, Xianfeng[4];Li, Yongjiang[3]

机构：[1]Zhanjiang Presch Educ Coll, Dept Math, Zhanjiang 524037, Peoples R China;[2]Sichuan Univ Sci & Engn, Coll Math & Stat, Zigong 643000, Peoples R China;[3]Guangdong Ocean Univ, Sch Math & Comp Sci, Zhanjiang 524025, Peoples R China;[4]Southwest Petr Univ, Sch Sci, Chengdu 610500, Peoples R China

年份：2023

卷号：11

期号：23

外文期刊名：MATHEMATICS

收录：SCI-EXPANDED(收录号：WOS:001116936400001)、、Scopus(收录号：2-s2.0-85178925517)、WOS

基金：Many thanks to the reviewers for their careful reading and helpful suggestions.

语种：英文

外文关键词：semi-flows; measure-preserving transformation; measurable sensitivity

外文摘要：Sensitive dependence on initial conditions is a crucial characteristic of chaos. The concept of measurable sensitivity (MS) was introduced as a measure-theoretic version of sensitive dependence on initial conditions. Their research demonstrated that MS arises from light mixing, indicates a finite number of eigenvalues for a transformation, and is not present in the case of infinite measure preservation. Unlike the traditional understanding of sensitivity, MS carries up to account for isomorphism in the sense of measure theory, which ignores the function's behavior on null sets and eliminates dependence on the chosen metric. Inspired by the results of James on MS, this paper generalizes some of the concepts (including MS) that they used in their study of MS for conformal transformations to semi-flows, and generalizes their main results in this regard to semi-flows.